Methods, apparatus and computer program for automatically deriving small-scale maps

ABSTRACT

One or more small-scale maps are generated automatically and directly from a single large-scale map or database. A subset of geographic features to be represented in the small-scale map is selected based on the scaling law. The geographic features in the subset are determined based on topological connectivity, size, bend size or point density characterizing the geographic features, so the subset includes the larger or more connected or with higher density among the geographic features.

BACKGROUND Technical Field

Embodiments of the subject matter disclosed herein generally relate toderiving small-scale maps from a large-scale map or database.

Discussion of the Background

Nowadays, people seldom use printed maps, preferring instead to usevarious computer displays. Computers have had significant positiveimpacts on enhancing the quality and quantity of information representedin maps. However, these improvements also pose a challenge because itbecomes difficult to meaningfully and clearly visualize all theinformation.

Any map is characterized by a map scale 1:M, which is a ratio between aunit on the map versus a real life-size M. For example, a 1:10,000 scalemeans that 1 cm on the map corresponds to 10,000 cm=100 m in real life.In a map, there is a minimum size, below which geographic featurescannot be clearly recognized. This is called minimum map unit. Allgeographic features represented in a map should be greater than theminimum map unit. Items represented on the maps—streets, lakes andrivers, buildings, etc.—are known as geographic features.

Theoretically, all the geographic features (which may be stored in adatabase) may be represented on a large and detailed enough map (calleda “large-scale map” in this document) characterized by an original scale1:M_(o). However, in practice, people frequently need maps with smallscales (i.e., less detailed) than the original scale. Simplistically,one may think that a small-scale map (characterized by a smaller scalethan the original scale) is merely a proportionally smaller version ofthe large-scale map. However, such a proportional approach sabotages theability to distinguish the geographic features, rendering theproportional small-scale map useless; see FIG. 8 for an illustration.

Conventionally, operator intervention has been employed to derivesmall-scale maps of a few limited scales rather than all scales, yeteven when assisted by software tools, it is a subjective andtime-consuming approach. Research has been carried out to derive a fewlimited scales of maps that involve often some geographic featuresrather than all geographic features. Overall, there is no automaticsolution to map generation of small scales, so in practice multiplescales of maps and databases are maintained. Thus it creates enormousdifficulties to maintain and update these maps and databases.

Another drawback in the conventional approach to generating maps withscales smaller than an original scale is that it is done step by step,with each map being obtained from its closest larger scale map. Thisstep-by-step approach can propagate errors from one map to the next.

Therefore, it is desirable to develop automated methods that avoidmaintaining and updating multiple scales of maps or databases, and avoidthe drawbacks of the conventional approach.

BRIEF SUMMARY

In various embodiments, small-scale maps with scales in a scale seriesare automatically derived from a single large-scale map or database in amanner based on the scaling law of the existence of far more smallthings than large ones, and a holistic view of all geographic features.Wherever possible, topological measures are given a higher priority thangeometric measures for selecting geographic features to be representedin small-scale maps. Unlike conventional maps, which are generalizedfrom their closet large-scale maps in a step-by-step fashion, each ofthe small-scale maps is generated directly from the single large-scalemap. This direct approach helps avoid error propagation. Quality ofsmall-scale maps is determined by the scaling law or all geographicfeatures themselves rather than subjectively determined by humancartographers.

According to an embodiment, there is a method for generating one or moresmall-scale maps from a single large-scale map or database. The methodincludes selecting a subset of geographic features to be represented inthe small-scale map. The number of geographic features and whatgeographic features are in the subset is automatically determined basedon the scaling law, and constrained by a minimum map unit. Thegeographic features in the subset are determined based on topologicalconnectivity or, size or bend size or density characterizing them so thesubset includes the more connected or larger or higher densitygeographic features. The method further includes generating thesmall-scale map using the subset of selected geographic features whilemaintaining topological relationships present in the single large-scalemap or database among the selected geographic features.

According to another embodiment, there is a map-generating apparatusconfigured to automatically generate one or more small-scale maps from asingle large-scale map or database. The apparatus has an interfaceconfigured to enable receiving input triggering one or more small-scalemaps to be generated and to output one or more small-scale maps, and adata processing unit. The data processing unit is connected to theinterface and configured to perform for each of the one or moresmall-scale maps and for each type of geographic features: (1) selectinga subset of geographic features to be represented in the small-scalemap, and (2) generating the small-scale map using the subset of selectedgeographic features while maintaining topological relationships presentin the single large-scale map or database among the selected geographicfeatures. The number of geographic features and what geographic featuresare in the subset are determined based on the scaling law, and thegeographic features in the subset are determined based on topologicalconnectivity or size or bend size or point density characterizing thegeographic features, so the subset includes the larger or more connectedor with higher density among the geographic features.

According to yet another embodiment, there is a non-transitorycomputer-readable recording medium storing executable codes which, whenexecuted by a processor having access to a large-scale map or database,generates one or more small-scale maps by performing for each one thefollowing steps: (1) selecting a subset of geographic features to berepresented in the small-scale map, and (2) generating the small-scalemap using the subset of selected geographic features while maintainingtopological relationships present in the single large-scale map ordatabase among the selected geographic features. The number ofgeographic features and what the geographic features are in the subsetare determined based on the scaling law and constrained by a minimum mapunit, and the geographic features in the subset are determined based ontopological connectivity or size or bend size or point densitycharacterizing the geographic features, so the subset includes thelarger or more connected or with higher density among the geographicfeatures.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate one or more embodiments and,together with the description, explain these embodiments. In thedrawings:

FIG. 1 illustrates a cartographic curve with plural recursively definedbends;

FIG. 2 is a map including 50,000 naturally defined cities;

FIG. 3 is the map in FIG. 2 in which lower-level cities or small citiesso to speak have been removed, yet this derived map is self-similar tothe map in FIG. 2;

FIG. 4 is a flowchart of a method according to an embodiment;

FIG. 5 is a sequence of Britain coastlines illustrating linesimplification based on bend size;

FIG. 6 is a graph of number of buildings versus map scale in a log-logplot;

FIG. 7 is a block diagram of a map-generating apparatus according to anembodiment;

FIG. 8 illustrate maps obtained by simply reducing map scales; and

FIG. 9 illustrates maps obtained with a method according to anembodiment.

DETAILED DESCRIPTION

The following description of the exemplary embodiments refers to theaccompanying drawings. The same reference numbers in different drawingsidentify the same or similar elements. The following detaileddescription does not limit the invention. Instead, the scope of theinvention is defined by the appended claims.

Reference throughout the specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with an embodiment is included in at least oneembodiment of the subject matter disclosed. Thus, the appearance of thephrases “in one embodiment” or “in an embodiment” in various placesthroughout the specification is not necessarily referring to the sameembodiment. Further, the particular features, structures orcharacteristics may be combined in any suitable manner in one or moreembodiments.

The embodiments described in this section automatically generate (i.e.,derive) small-scale maps directly from a single large-scale map ordatabase. The small-scale maps are characterized by derived scales1:M_(d) that are smaller than the original scale (i.e., M_(d) is largerthan M_(o)). The small-scale maps represent only a subset of thegeographic features in the large-scale map or database. The geographicfeatures in the subset are selected using the scaling law as explainedbelow.

A series of scales, including scales for which M_(d)/M_(o) aresuccessive powers of 2, are defined as primary scales. For example, ifthe original scale is 1:1,000 (this original scale value is merelyillustrative and not intended to be limiting), then primary scales are1:2,000, 1:4,000, 1:8,000, 1:16,000, 1:32,000, 1:64,000, 1:128,000,1:256,000, 1:512,000, 1:1,024,000, 1:2,048,000, 1:4,096,000,1:8,192,000, 1:32,768,000.

In this context, the minimum scale 1:M_(m) is the smallest scale in theseries of scales. For a city, the minimum scale is 1:1,024,000corresponding to a 2¹⁰ ratio M_(m)/M_(o). For a country, the minimumscale is 1:4,096,000 corresponding to a 2¹² ratio M_(m)/M_(o). For theentire world, the minimum scale is 1:32,768,000 corresponding to a 2¹⁵ratio M_(m)/M_(o). Note that here, city is not arbitrarily defined basedon tradition or administrative rules, but it is rather a natural city. Anatural city is naturally derived city boundary based on massivegeographic information, e.g., all street nodes or junctions of an entirecountry. All these nodes firstly constitute a triangulated irregularnetwork (TIN). All the edges of the TIN demonstrate a heavy taileddistribution. Using head/tail breaks, we partition all the TIN edgesinto two parts: those below the average length called the tail, andthose above the average called the head. All the edges in the tailconstitute natural cities.

As previously mentioned, the term “geographic features” refers tomeaningful geographic objects or spatially coherent entities such asstreets, buildings and cities. The term does not refer to geometricobjects such as pixels, points, lines and polygons that may be used torepresent the geographic features on maps. The term “streets” refers toentire natural streets rather than street segments between twointersections. Here, natural streets are made of segments joined basedon good continuity rule (e.g., from each segment, a next segment is theone with smallest deflection angle, all segments being eventually mergedto create natural streets).

Scaling law refers to the fact that in a geographic space there are farless significant or relevant geographic features than significant orrelevant ones. The manner of assessing significance or relevance dependson the type of geographical feature. For example, if the significance orrelevance assessment is based on connectivity (as suitable for streets),there are far more less-connected geographic features thanwell-connected geographic features. In another example, if thesignificance or relevance assessment is based on size (e.g., height,surface or volume for buildings), there are far more small geographicfeatures than large geographic features on the Earth's surface (andtherefore, far more small symbols than large ones in any map).Semantically, the scaling law states that there are far more meaninglessthings than meaningful ones.

Under the scaling law, the Gaussian view, which assumes that geographicfeatures are more or less similar (and therefore have similar attributevalues), is replaced by a Paretian way of thinking that geographicfeatures' attribute values have underlying skewed distributions such aspower laws, Pareto and lognormal distributions. Such a distribution maybe better characterized by head/tail breaks in order to derive theunderlying scaling hierarchy of numerous smallest, a very few largest,and some in between the smallest and the largest. The head/tail breaksworks as follows. Given an attribute (number of connections, height,surface, volume, etc.) of geographic features whose distribution isright skewed, a mean value of the attribute values is calculated first.The geographic features are then split in two groups: a first group(“the head”) includes the geographic features having large (above themean) attribute values, and a second group (“the tail”) includes thegeographic features having small (below the mean) attribute values. Thegeographic features in the first group are a minority (e.g., less than40%), while the geographic features in the second group are a majority.

The same head/tail breaks process is then performed for the geographicfeatures in the first group (the head). Progressively and iteratively,the geographic features are analyzed in the same manner until theattribute values of the geographic objects in the head group no longermeet the condition of far more small things than large ones.

For example, streets are characterized by their respective number ofconnections with other streets. Based on a rank-size plot for thenumbers of connections (which is right skewed, as far more streets areless-connected than well-connected), the streets can be split (accordingto head/tail breaks under the scaling law) into streets (T1) havingfewer than average number of connections, and streets (H1) having morethan average number of connections. The streets in T1 have lowest level(i.e., level 1), and are the first group of streets to be discarded (nolonger represented) in a small-scale map.

If H1 still has a skewed rank-size plot of the numbers of connections,the streets in H1 are then split into H2 and T2. The streets in T2 havenext-to-lowest level (i.e., level 2), and are the second group ofstreets to no longer be represented in a small-scale map. If H2 stillhas a skewed rank-size plot of the number of connections, the streets inH2 are split into H3 and T3, etc.

This way, both the number of levels and the interval of values for eachlevel are naturally and automatically derived. The number of levels, orequivalently the ht-index, indicates hierarchical levels of thegeographic features based on their attribute values.

Bends in a cartographic curve may be analyzed in a similar manner. Abend is a basic unit of a curve or part of a polygon representing alinear geographic feature such as a highway or a lake. The small bendsin such a curve are far more numerous than the large ones. For example,the cartographic curve illustrated in FIG. 1 has seven bends x₁-x₇.Since bends x₁, x₂, x₃ are far larger than small bends x₄, x₅, x₆, x₇,the former are in the head group and the latter in the tail group (level1). Focusing now on the bends in the head group, bend x₁ is far largerthan bends x₂, x₃. Therefore, bend x₁ is in a second head group, whilebends x₂ and x₃ are in a second tail group (level 2). Since the secondhead group has only one member (i.e., x₁, which has level 3) thehead/tail breaks process cannot continue. Since the head/tail breaksworked twice for the bends of the cartographic curve in FIG. 1, thecartographic curve has an ht-index h(x)=3, and x₁-x₇ levels are 3, 2, 2,1, 1, 1, and 1 respectively.

To summarize, head/tail breaks is used for determining levels ofgeographic features of the same type (characterized by values of a sameattribute) and an ht-index of the geographic features whose attributevalues form heavy-tailed (i.e., right-skewed) distributions. Thegeographic features are divided into a very few geographic featurescharacterized by large attribute values (corresponding, e.g., to largeor well-connected streets) in a head group, and numerous geographicfeatures characterized by small attribute values in the tail group.Recursively, the focus shifts to the geographic features in the headgroup, which are again divided if their attribute values form aheavy-tailed distribution, until the distribution of the head geographicfeatures no longer has a heavy tailed distribution.

FIGS. 2 and 3 illustrate the visualization impact of removing lesssignificant (lower levels) geographic features. FIG. 2 is a Germany mapwith 50,000 cities. Analysis of the distribution of these cities' pointsof interest splits them in seven levels (i.e., ht-index is 7). FIG. 3shows only the cities that have the higher four levels (i.e., not in thetails of the initial distribution and two subsequent distributions).FIG. 3, where the less significant (lower levels) cities have beenremoved, exhibits a pattern corresponding to the underlying citiespattern or structure in FIG. 2, but also enables the viewer todistinguish its scaling pattern of far more small cities than largeones.

In this document, the term “topology” refers to topologicalrelationships between geographic features, so its meaning is differentfundamentally from the same notion used in geographic informationsystems (GIS). In the GIS literature, topology refers to therelationship between geometric elements such as pixels, points, lines,and polygons. Here, topology used in this document enables visualizationof the underlying scaling of far more less-connected things thanwell-connected ones, or far more small things than large ones ingeneral.

FIG. 4 is a flow diagram of a method 400 for automatically (withoutoperator intervention) generating one or more small-scale maps directlyfrom a single large-scale map or database. Automatic generation ofsmall-scale maps is based on a holistic view of the geographic spaceinvolving all the geographic features therein. The maps may represent anentire country, if not an entire continent or the entire world.Alternatively or additionally, the mapping target may be a city. Thecity is not arbitrarily defined (e.g., by government), but naturallyderived from the country as whole. Natural cities are thus sub-wholes ofthe country. The larger the area covered by the large-scale map ordatabase (e.g., the country) the more striking the scaling law applies.

The method may generate any small-scale map characterized by a scalesmaller than the original scale. The scale may have a value in a seriesof scale values as the previously-described primary scales. Two or moresmall-scale maps may be derived simultaneously. All the small-scale mapsare derived directly from the large-scale map or database. Steps 410 and420 described below are performed automatically for each small-scale mapthat method 400 generates.

At 410, geographic features to be represented in the small-scale map areselected according to the scaling law. The selected geographic featuresare a subset of the geographic features in the large-scale map ordatabase. Geographic features of each geographical feature type (i.e.,characterized by a different attribute) are treated separately.

If the geographic features are associated with a degree of connectivity,then connectivity rather than their size is used to select thegeographic features to be represented in the small-scale map. Whichlevels (i.e., groups of the connected geographic features ranging fromthe least connected at level 1 to the most connected at a level equal tothe ht-index) to be represented on maps of different scales isdetermined holistically based on the ht-index obtained as previouslydescribed. Formally, the level of geographic features above which to berepresented in a map of scale 1:M_(d) is calculated as follows:

$\begin{matrix}{T = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(c)}}} & (1)\end{matrix}$

where h(c) is the ht-index of a degree of connectivity of all connectedgeographic features of a certain type. Equation (1) can be modifiedslightly by changing h(c) to h(x) for example to be applied to thegeographical features characterized by other attributes (such as size,bend size and point density) as long as the attribute values yield aheavy tailed distribution; see the below formulas (2) and (3).

The reduction in the number of geographic features in a small-scale mapusing the above-described technique is smaller in the conventionalapproach (an empirical Töpfer's law derived from map sheets rather thana whole like a country). For example, from level to level, thescaling-law-based approach yields a reduction to 40% in the number ofgeographic features, while the conventional approach yields a reductionto about 70%.

Method 400 further includes, at 420, generating the small-scale mapusing the subset of geographic features while maintaining thetopological relationships present in the single large-scale map ordatabase among the selected geographic features. In case the topologicalrelationships changed in the small-scale map, operations such asdisplacement and merging must apply in order to maintain these initialtopological relationships. For example, the two parallel streets in thelarge-scale map are separated from each other, in the small-scale mapmay be merged. In another example, one street and one lake are disjointin the large-scale map, in the small-scale map seem to overlap. In thiscase, the lake is displaced in order to avoid it overlapping the street.

In some embodiments, linear geographic features characterized bygeographic details associated with different levels are simplified. Forexample, the cartographic curve in FIG. 1 has an ht-index=3. Thegeometric details represented in a small-scale map having the scale1:M_(d) are selected to be associated with a level larger than

$\begin{matrix}{G = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {{h(x)}.}}} & (2)\end{matrix}$

where h(x) is the ht-index of all bends of a cartographic curve orpolygon.

A polygon is considered to consist of two cartographic curves resultingfrom partitioning the polygon along its longest axial direction. Forexample, if M_(d)/M_(o)=2⁵ and M_(d)/M_(o)=2¹⁰, then G=1.5 for thecartographic curve in FIG. 1. Therefore, in the small-scale map of scale1:M_(d) only bends x₁, x₂, x₃ are represented. If the small-scale map ischaracterized by the minimum scale M_(d)=M_(m), geometric detail G=h(x)(=3 for the cartographic curve in FIG. 1), which means that only highestlevel details are illustrated (e.g., only bend x₁ together with the twoending points is represented for the cartographic curve in FIG. 1).Conversely, in the map having the original scale M_(d)=M_(o), G=0, whichindicates that all the details starting at the lowest level areillustrated, thus, no simplification at all. For all other scalesbetween the roughest and the most detailed, geometric detail G isbetween 0 and h(x), i.e., 0<G<h(x). FIG. 5 illustrates the effect ofgradual removal of small bends (level by level) for the Britaincoastline.

The same holistic approach is applied when the geographic features arepoint-like features (e.g., points of interest such as bus stops,locations of churches and schools) with different densities. In order toselect which of the point-like geographic features are to be representedin a small-scale map, a triangulated irregular network (TIN) is createdconsidering all the point-like features in the large-scale map ordatabase. The reciprocal of the TIN edges follow a heavy taileddistribution, indicating that there are far more low-density points thanhigh-density points. Every point-like geographic feature is thenassociated with a hierarchical level, and the level of points to berepresented in a small-scale map having the scale 1:M_(d) is

$\begin{matrix}{P = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {{h(\rho)}.}}} & (3)\end{matrix}$

where h(ρ) is the ht-index of all densities of individual points as awhole.

Formulas (1)-(3) are simpler to evaluate when the ratio of the scaledenominators is powers of 2, but they may in principle be applied forany scale. The number of geographic features of a certain type forsmall-scale maps whose scale is not in a power of 2 ratio with theoriginal scale may be evaluated in the following manner. The number ofgeographic features of a certain type is evaluated for every of theprimary scales. Then, using this number, a power law y=Nr^(−c) isestablished, where y is the number of geographic features of a certaintype in a small-scale map (known for every of the primary scales), N isa constant, r is the primary scale as a variable and c is called powerlaw exponent. Establishing the power law basically means calculating thconstant N, and exponent c. The relationship is then used to calculatethe number of geographic features of the certain type in a map of anyscale. For example, FIG. 6 is a graph of the number of buildings versusscale in a log-log plot for a power law y=129,241 r^(−1.65). This powerlaw can determine the number of buildings with any map scale in therange. Once the number is established, the subset of buildings isselected from the largest to smaller ones up to the determined number.

An advantage of the above-described technique for generating one or moresmall-scale maps is that, unlike the conventional approach, each of themaps is derived directly from the single large-scale map or database.This direct derivation avoids the problem of error propagation.

The above-discussed procedures and methods may be implemented in amap-generating apparatus as illustrated in FIG. 7. Hardware, firmware,software or a combination thereof may be used to perform the varioussteps and operations described herein. Map-generating apparatus 700 ofFIG. 7 is an exemplary computing structure that may be used toautomatically generate small-scale maps from a single large-scale map ordatabase. Map generation according to the above-described methods isboth computational- and data-intensive processes, for it engages of allgeographic features of all types of an entire country. Testing for cityof Stockholm (illustrated in FIG. 9) has been performed on a powerfuldesktop with 32 GB RAM, and a 1 TB hard disk, and it took 20 hours forthe computer to generate 10 primary scales of maps. Therefore cloud- orgrid-computing facilities may be employed for the map generation at acountry scale.

Exemplary map-generating apparatus 700 includes a server 701 with acentral processor (CPU) 702 coupled to a random access memory (RAM) 704and to a read-only memory (ROM) 706. ROM 706 may also be other types ofstorage media to store programs, such as programmable ROM (PROM),erasable PROM (EPROM), etc.

Processor 702 may communicate with other internal and externalcomponents through input/output (I/O) circuitry 708 and bussing 710 toprovide control signals and the like. Processor 702 carries out avariety of functions as are known in the art, as dictated by softwareand/or firmware instructions.

Server 701 may also include one or more data storage devices, includinghard drives 712, CD-ROM drives 714 and other hardware capable of readingand/or storing information, such as DVD, etc. In one embodiment,software (i.e., executable codes) for carrying out the above-discussedmethods may be stored and distributed on a CD-ROM or DVD 716, a USBstorage device 718 or other form of media capable of portably storinginformation. These storage media may be inserted into, and read by,devices such as CD-ROM drive 714, disk drive 712, etc. Server 701 may becoupled to a display 720, which may be any type of known display orpresentation screen, such as LCD, plasma display, cathode ray tube(CRT), etc.

A user input interface 722 including one or more user interfacemechanisms such as a mouse, keyboard, microphone, touchpad, touchscreen, voice-recognition system, etc., is also provided. Server 701 maybe coupled to other devices, such as sources, detectors, etc. The servermay be part of a larger network configuration as in a global areanetwork (GAN) such as the Internet 728.

Quality of derived-scale maps is based on the scaling property of farmore small geographic features than large ones, or far moreless-connected geographic features than well-connected ones, and it isnot affected by human subjective intervention. Therefore, derived mapsquality is a matter of fact, little of human opinion. The enhancedquality is visible comparing FIG. 8 with FIG. 9. The panels in FIG. 8illustrate maps obtained by simply reducing map scale without anyselection or simplification, while the panels in FIG. 8 illustrate mapsobtained with the automatic methods described in this section. Theupper-left corner panel is a fragment of the large-scale map, the onenext to the right is a derived map with scale a half of the originalscale, the next one to the right is a derived map with scale one quarterof the original scale, etc. (the map scales decrease along each row andfrom one row to the next).

The disclosed exemplary embodiments provide methods and apparatus forautomatically generating a series of small-scale maps from a singlelarge-scale map or database based on the scaling law. It should beunderstood that this description is not intended to limit the invention.On the contrary, the exemplary embodiments are intended to coveralternatives, modifications and equivalents, which are included in thespirit and scope of the invention as defined by the appended claims.Further, in the detailed description of the exemplary embodiments,numerous specific details are set forth in order to provide acomprehensive understanding of the claimed invention. However, oneskilled in the art would understand that various embodiments may bepracticed without such specific details.

Although the features and elements of the present exemplary embodimentsare described in the embodiments in particular combinations, eachfeature or element can be used alone without the other features andelements of the embodiments or in various combinations with or withoutother features and elements disclosed herein.

This written description uses examples of the subject matter disclosedto enable any person skilled in the art to practice the same, includingmaking and using any devices or systems and performing any incorporatedmethods. The patentable scope of the subject matter is defined by theclaims, and may include other examples that occur to those skilled inthe art. Such other examples are intended to be within the scope of theclaims.

What is claimed is:
 1. A method for generating one or more small-scalemaps from a single large-scale map or database, the method comprising,for each of the one or more small-scale maps and for each type ofgeographic features automatically performing: selecting a subset ofgeographic features to be represented in the small-scale map, wherein anumber of geographic features in the subset is determined based on ascaling law, and the geographic features in the subset are determinedbased topological connectivity or size or bend size or point densitycharacterizing the geographic features, so as the subset to includelarger or more connected among the geographic features; and generatingthe small-scale map using the subset made of selected geographicfeatures, while maintaining topological relationships present in thesingle large-scale map or database among the selected geographicfeatures.
 2. The method of claim 1, wherein the single large-scale mapor database includes geographic features related to a country, acontinent or entire world.
 3. The method of claim 1, wherein each of theone or more small-scale maps is characterized by a small-map scale in ascale series, a denominator of the small-map scale being larger than adenominator of an original scale associated with the single large-scalemap or database.
 4. The method of claim 3, wherein a ratio of thesmall-scale denominator and the denominator of the original scale is apower of
 2. 5. The method of claim 4, wherein if the area is a city, adenominator of a minimum scale in the scale series is 2¹⁰; if the areais a country, the denominator of the minimum scale in the scale seriesis 2¹², and if the area is entire world, the denominator of the minimumscale the scale series is 2¹⁵.
 6. The method of claim 1, wherein thegeographic features characterized by number of connections are splitinto levels using head/tail breaks, and the topological connectivity Tindicating a lowest level of the selected geographic features in thesmall-scale map with a scale denominator M_(d) is calculated as$T = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(c)}}$where M_(o) is an original scale denominator of the large-scale map ordatabase, M_(m) is a denominator of a minimum-scale in a scale series,and h(c) is an ht-index of topological connectivity of all connectedgeographic features of a certain type.
 7. The method of claim 1, whereina selected geographic feature is simplified in the small-scale map witha scale denominator M_(d) by using geometric details of levels higherthan and equal to G calculated as$G = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(x)}}$where h(x) is an ht index of all bends of the selected geographicfeature, M_(o) is a denominator of an original scale associated with thesingle large-scale map or database, and M_(m) is a denominator of aminimum scale in a scale series that includes the small-map scale. 8.The method of claim 1, wherein the selecting is performed separately forpoint-like geographic features, each of the point-like features beingassociated with a hierarchical level, and point-like geographic featuresincluded in the subset having higher hierarchical levels than point-likegeographic features not included in the subset, the hierarchical level Pbeing calculated as$P = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(\rho)}}$where M_(d) is a denominator of a small-map scale, M_(o) is adenominator of an original scale associated with the single large-scalemap or database, M_(m) is a denominator of a minimum scale in a scaleseries that includes the small-map scale, and h(ρ) is an ht-index ofdensity of point-like geographic features.
 9. The method of claim 1,further comprising determining a constant c in a power law y=Nr^(−c)based on a number y of geographic features of a predetermined type inthe subset of a primary-scale map, N being a constant, and r being aprimary scale; and calculating a number y₂ of geographic features of thepredetermined type of the small-scale characterized by a scale r₂ asy₂=Nr^(−c).
 10. A map-generating apparatus configured to automaticallygenerate one or more small-scale maps from a single large-scale map ordatabase, the apparatus comprising: an interface configured to enablereceiving input triggering the one or more small-scale maps to begenerated and to output the one or more small-scale maps; and a dataprocessing unit connected to the interface and configured to perform foreach of the one-or more small-scale maps selecting a subset ofgeographic features to be represented in the small-scale map, wherein anumber of geographic features in the subset is determined based on ascaling law, and the geographic features in the subset are determinedbased topological connectivity or size or bend size or point densitycharacterizing the geographic features, so as the subset to includelarger or more connected among the geographic features; and generatingthe small-scale map using the subset made of selected geographicfeatures, while maintaining topological relationships present in thesingle large-scale map or database among the selected geographicfeatures.
 11. The apparatus of claim 10, wherein the single large-scalemap or database includes geographic features related to a country, acontinent or entire world.
 12. The apparatus of claim 10, wherein eachof the one or more small-scale maps is characterized by a small-mapscale in a scale series, a denominator of the small-map scale beinglarger than a denominator of an original scale associated with thesingle large-scale map or database.
 13. The apparatus of claim 12,wherein a ratio of the small-scale denominator and the denominator ofthe original scale is a power of
 2. 14. The apparatus of claim 13,wherein if the area is a city, a denominator of a minimum scale in thescale series is 2¹⁰; if the area is a country, the denominator of theminimum scale in the scale series is 2¹², and if the area is entireworld, the denominator of the minimum scale the scale series is 2¹⁵. 15.The apparatus of claim 10, wherein the data processing unit isconfigured to split the geographic features characterized by number ofconnections into levels using a head/tail breaks technique, and tocalculate the topological connectivity T indicating a lowest level ofthe selected geographic features as$T = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(c)}}$where M_(d) is a scale denominator of the small-scale map, M_(o) is anoriginal scale denominator of the large-scale map or database, M_(m) isa denominator of a minimum-scale in a scale series, and h(c) is anht-index of topological connectivity of all connected geographicfeatures of a certain type.
 16. The apparatus of claim 10, wherein thedata processing unit is configured to simplify a selected geographicfeature using geometric details of level higher than and equal to Gcalculated as$G = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(x)}}$where h(x) is an ht index of all bends of the selected geographicfeature, M_(d) is a denominator of a small-map scale, M_(o) is adenominator of an original scale associated with the single large-scalemap or database, and M_(m) is a denominator of a minimum scale in ascale series that includes the small-map scale.
 17. The apparatus ofclaim 10, wherein the data processing unit is configured to selectseparately point-like geographic features, each of which is associatedwith a hierarchical level calculated for the point-like geographicfeatures, so as point-like geographic features included in the subsethave higher hierarchical levels than point-like geographic features notincluded in the subset, the hierarchical level P being calculated as$P = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(\rho)}}$where M_(d) is a denominator of a small-map scale, M_(o) is adenominator of an original scale associated with the single large-scalemap or database, M_(m) is a denominator of a minimum scale in a scaleseries that includes the small-map scale, and h(ρ) is an ht-index ofdensity of point-like geographic features.
 18. The apparatus of claim10, wherein the data processing unit is further configured: to determinea constant c in a power law y=Nr^(−c), based on a number y of geographicfeatures of a predetermined type in the subset of a primary-scale map, Nbeing a constant, and r being a primary scale r; and to calculate anumber y₂ of geographic features of the predetermined type of thesmall-scale characterized by a scale r₂ as y₂=Nr^(−c).
 19. Anon-transitory computer-readable recording medium storing executablecodes which, when executed by a processor having access to a large-scalemap or database, generate one or more small-scale maps by performing foreach of the one or more small-scale maps and for each type of geographicfeatures: selecting a subset of geographic features to be represented inthe small-scale map, wherein a number of geographic features in thesubset is determined based on a scaling law, and the geographic featuresin the subset are determined based topological connectivity or size orbend size or point density characterizing the geographic features, so asthe subset to include larger or more connected among the geographicfeatures; and generating the small-scale map using the subset made ofselected geographic features, while maintaining topologicalrelationships present in the single large-scale map or database amongthe selected geographic features.
 20. The non-transitorycomputer-readable recording medium, wherein the executable codes furthermake the processor to perform at least one of: to split the geographicfeatures characterized by number of connections are split into levelsusing a head/tail breaks technique, and to calculate the topologicalconnectivity T indicating a lowest level of the selected geographicfeatures in the small-scale map with a scale denominator M_(d) iscalculated as$T = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(c)}}$where M_(o) is an original scale denominator of the large-scale map ordatabase, M_(m) is a denominator of a minimum-scale in a scale series,and h(c) is an ht-index of topological connectivity of all connectedgeographic features of a certain type; to simplify a selected geographicfeature in the small-scale map by using geometric details of levelshigher than and equal to G which is calculated as$G = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(x)}}$where h(x) is an ht index of all bends of the selected geographicfeature; and to select point-like geographic features separately, eachof the point-like features being associated with a hierarchical level,and point-like geographic features included in the subset having higherhierarchical levels than point-like geographic features not included inthe subset, the hierarchical level P being calculated as$P = {\frac{\log_{2}\left( \frac{M_{d}}{M_{0}} \right)}{\log_{2}\left( \frac{M_{m}}{M_{0}} \right)} \times {h(\rho)}}$where h(ρ) is an ht-index of density of point-like geographic features.